Returns the downside deviation of a given data set.

## Syntax

NxDWS(**[x]**,m)

- [x]
- is the portfolio simple rate of returns data series (a one-dimensional array of cells (e.g., rows or columns)).
- m
- is the minimum acceptable return (MAR). If missing, a zero (0) value is assumed.

* * Status

The NxDWS function is available starting with NumXL version 1.68 CAMEL.

## Remarks

- The downside deviation (DWS) measures downside risk and focuses on returns below a minimum threshold or acceptable return (MAR).
- The DWS is an indicator used to assess the relative riskiness of one investment fund or strategy versus another.
- By definition, all values in the input data set (i.e., X) must be greater than -1.0.
- The input data series may include missing values (e.g., #N/A, #VALUE!, #NUM!, empty cell) but will not be included in the calculations.
- The DWS is computed as follows:

$$\textrm{DWS}= \sqrt{\frac{\sum_{i=1}^{N}{G(r_i)}}{N}}$$

$$G(r_i)=\left\{\begin{matrix} (r_i-r_m)^2 & r_i<r_m\\ 0 & ri \geqslant r_m \end{matrix}\right. $$

Where:

- $N$ is the number of data points with non-missing values.
- $r_i$ is the simple return for the i-th data point.
- $r_m$ is the minimum acceptable return (MAR).

## Files Examples

## Related Links

## References

- Hamilton, J .D.; Time Series Analysis, Princeton University Press (1994), ISBN 0-691-04289-6
- Tsay, Ruey S.; Analysis of Financial Time Series John Wiley & SONS. (2005), ISBN 0-471-690740

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